In a threading operation using an NC system, as is well known, a threading workpiece is held by a chuck provided in the main spindle, the threading workpiece is rotated by the main spindle being rotated, and a cutter (turning tool) moved by a servo spindle driven by a feeding servo motor is moved axially (Z-axis direction) so as to be synchronized with the rotation of the main spindle. However, if the rotation of the main spindle and the Z-axis direction movement of the cutter are not synchronized, the dimensional accuracy of the thread is degraded, or a double thread is formed or the ridge is damaged in finish machining.
Therefore, in the threading operation, it is required, for instance, to start moving the cutter in the Z-axis direction based on a single-rotation signal generated in every rotation of the main spindle, and to synchronize the rotation of the main spindle with the feeding of the cutter.
In addition, in transitioning from rough machining to finish machining, for example, when the rotational speed of the main spindle is increased a predetermined number of times, the feed rate of the cutter is also increased the predetermined number of times in order to synchronize the rotation of the main spindle and the feeding of the cutter. However, at this time, discrepancy occurs between the servo delay in the feed rate (low speed) of the cutter in the rough machining and the servo delay in the feed rate (high speed) of the cutter in the finish machining, so that thread phase displacement arises.
For this reason, a method has been disclosed in Japanese Patent Laid-Open No. 177252/1983, in which, given that an amount of servo delay for the feeding motor actual speed in the finish machining to reach fL (feed rate in finishing) is dL (=fL/k, where k is a gain in the servo system), and the main-spindle rotational speed is θL, by positioning the cutter stop position before the finish machining apart from the workpiece by above dL, the actual speed reaches the constant speed fL at the rotational angle θL after generation of a single-rotation signal, and the threading is started from the rotational angle θL at the constant speed fL; meanwhile, given that an amount of the servo delay for the feeding motor actual speed in the rough machining to reach fs (feed rate in rough machining, fs<fL) is ds (=fs/k, where k is a gain in the servo system), and the main-spindle rotational speed is θs, by positioning the cutter stop position before the rough machining apart from the workpiece by above ds, the actual speed reaches the constant speed fs at the rotational angle θL after generation of a single-rotation signal, and the threading is started from the rotational angle θL at the constant speed fs.
Moreover, a method has been disclosed, in which, introducing the above-described idea, even if the cutter stop position before starting threading in the finish machining is identical to that in the rough machining, by controlling the generation point of the single-rotation signal of the main spindle, when performing the finish machining, the threading is started from the rotational angle θL at a constant speed fL, meanwhile, when performing the rough finish machining, the threading is started from the rotational angle θL at a constant speed fs.
In short, in Japanese Patent Laid-Open No. 177252/1983, a technology is disclosed, in which thread phase displacement is prevented by taking into account the amount of the servo delay, even if the rotational speed of the feeding motor is variable.
Moreover, as a conventional technology regarding remachining of a thread, there is a technology disclosed in Japanese Patent Laid-Open No. 99020/1987.
In the technology, in remachining a thread, an amount of phase displacement of the thread groove in the threaded portion, generated in mounting the threaded workpiece, is measured; the amount of delay in the servo system for the numerical control machine tool and the computational delay time in the numerical control system (delay amount from the detection of the pulse data of the main-spindle rotational frequency to the completion of the computation) are computed; based on the above-described phase displacement, the above-computed delay in the servo system, and the above-computed computational delay time, the phase displacement amount is calculated; and the phase of the above-described threaded portion is aligned based on the phase displacement amount, to remachine the threaded portion.
With regard to the phase displacement amount, the actual phase displacement amount δt is calculated according to the following equation from the phase displacement amount of the threaded portion δi (mm) generated by remounting the workpiece, the delay amount of the servo system SD (mm), the delay amount S1 from the detection of the pulse data of the main-spindle rotational frequency to the completion of the computation, and the servo feed rate F.δt=remainder of (δi+S1+SD)/F 
Here, F is calculated as below.F=(thread pitch command)×(main-spindle rotational frequency)
In Japanese Patent Laid-Open No. 99020/1987, a technology as above is disclosed.
Meanwhile, in the conventional technology (the technology disclosed in Japanese Patent Laid-Open No. 177252/1983), as described above, only the servo system delay has been considered in order to prevent thread phase displacement, so that a problem has been that thread phase displacement still arises.
Incidentally, in the above-described technology (the technology disclosed in Japanese Patent Laid-Open No. 177252/1983), because only the servo system delay has been considered, if the acceleration time-constant when the servo feed rate is (servo feed rate)A (in finish machining of the thread) is identical to that when the servo feed rate is (servo feed rate)B (in rough machining of the thread), then thread phase displacement due to the acceleration/deceleration time-constant arises between when the servo feed rate is (servo feed rate)A (in finish machining of the thread) and when the servo feed rate is (servo feed rate)B (in rough machining of the thread) as illustrated in FIG. 6.
Moreover, also in the thread remachining technology disclosed in Japanese Patent Laid-Open No. 99020/1987, the amount of the phase displacement of the threaded portion, generated by remounting the workpiece, the servo system delay amount, and the delay amount from the detection of the pulse data of the main-spindle rotational frequency to the completion of the computation have only been considered, so that the thread phase displacement 44 due to the acceleration/deceleration time-constant arises as illustrated in FIG. 7.
In addition, FIG. 7 illustrates an example of a linear acceleration/deceleration profile, in which numeral 41 denotes a stepped command-feed-rate profile commanded by a program; numeral 42 denotes an output speed profile to the servo, accelerated/decelerated by a time constant Tc based on the command; numeral 43 denotes a servo operational speed profile, delayed by the servo response delay; numeral 45 denotes an amount of the phase displacement due to the servo response delay; and numeral 44 denotes the thread phase displacement amount due to the acceleration/deceleration time-constant.